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Unit 1 - Limits

Terms in this set (22)

Asymptote
a line or curve that the graph of a relation approaches more and more closely the further the graph is followed
Continuous Function
a function with a connected graph
Discontinuity
"a point at which the graph of a relation or function is not connected
can be classified as either removable or essential (nonremovable)"
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Discontinuous Function
a function with a graph that is not connected
End Behavior
the appearance of a graph as it is followed farther and farther in either direction
Hole
a point at which the limit of the function exists but does not equal the value of the function at that point
Infinite Limit
a limit that has an infinite result
Infinity
a number which indicates a quantity, size, or magnitude that is larger than any real number
Intermediate Value Theorem
If f is a function that is continuous over the domain [a,b] and if m is a number between f(a) and f(b), then there is some number c between a and b such that f(c)=m.
Jump Discontinuity
a discontinuity for which the limits from the left and right both exist but are not equal to each other
Limit
value that a function or expression approaches as the domain variable(s) approach a specific value
Limit at Infinity
a limit taken as the variable approaches infinity or negative infinity
Limit from the Left
a limit taken as the variable approaches only from the left
Limit from the Right
a limit taken as the variable approaches only from the right
Limits of Integration
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One-Sided Limit
either a limit from the left or a limit from the right
Removable Discontinuity
a point at which the limit of the function exists but does not equal the value of the function at that point
Pinching/Sandwich/Squeeze Theorem
a theorem which allows the computation of the limit of an expression by trapping the expression between two other expressions which have limits that are easier to compute
Solve Analytically
use algebraic and/or numeric methods as the main technique for solving
Solve Graphically
use graphs and/or pictures as the main technique for solving
Step Discontinuity
a discontinuity for which the limits from the left and right both exist but are not equal to each other
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